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A photographer wants to take a picture of a lighthouse with the full moon as background, but he wants the full moon and the lighthouse to be about the same size. The light house has a height of 22 meters, and the moon subtends an angle of about 0.53 degrees of arc to an observer on the Earth. How far from the lighthouse should the photographer place the camera to get the picture?
Solution:
Using the following image as reference, we know that the height of the lighthouse,
y, is 22 meters and that
the angle θ has to be the same as for the moon, 0.53 degrees. The distance from the camera to the
lighthouse is given by x. The trigonometric equation for the tangent of an angle is
tan(θ) = y/x. Thus, x = y/tan(θ) = 22 meters/0.00925 = 2,378 meters.
Note: When using a calculator for the tangent make sure to set it for degrees and not radians.
The photographer has to place the camera approximately 2.4 kilometers from the lighthouse.
